Conical intersections adiabatic representation

Single surface calculations with a vector potential in the adiabatic representation and two surface calculations in the diabatic representation with or without shifting the conical intersection from the origin are performed using Cartesian coordinates. As in the asymptotic region the two coordinates of the model represent a translational and a vibrational mode, respectively, the initial wave function for the ground state can be represented as. 

Single surface calculations with proper phase treatment in the adiabatic representation with shifted conical intersection has been performed in polai coordinates. For this calculation, the initial adiabatic wave function tad(9, 4 > o) is obtained by mapping t, to) ittlo polai space using the relations,... 

H3 (and its isotopomers) and the alkali metal triiners (denoted generally for the homonuclears by X3, where X is an atom) are typical Jahn-Teller systems where the two lowest adiabatic potential energy surfaces conically intersect. Since such manifolds of electronic states have recently been discussed [60] in some detail, we review in this section only the diabatic representation of such surfaces and their major topographical details. The relevant 2x2 diabatic potential matrix W assumes the fomi... 

Yarkony DR (2001) Nuclear dynamics near conical intersections in the adiabatic representation. I. The effects of local topography on interstate transition. J Chem Phys 114 2601... 

Density functional theory, direct molecular dynamics, complete active space self-consistent field (CASSCF) technique, non-adiabatic systems, 404-411 Density operator, direct molecular dynamics, adiabatic systems, 375-377 Derivative couplings conical intersections, 569-570 direct molecular dynamics, vibronic coupling, conical intersections, 386-389 Determinantal wave function, electron nuclear dynamics (END), molecular systems, final-state analysis, 342-349 Diabatic representation ... 

Single surface calculations with proper phase treatment in the adiabatic representation with shifted conical intersection has been performed in polar coordinates. For this calculation, the initial adiabatic wave function bad(< , to) is obtained by mapping 4 a and R Rq = qcas < x At this point, it is necessary to mention that in all the above cases the initial wave function is localized at the positive end of the R coordinate where the negative and positive ends of the R coordinate are considered as reactive and nonreactive channels. 

Appendix C On the Single/Multivaluedness of the Adiabatic-to-Diabatic Transformation Matrix Appendix D The Diabatic Representation Appendix E A Numerical Study of a Three-State Model Appendix F The Treatment of a Conical Intersection Removed from the Origin of Coordinates Acknowledgments References... 

In principle, the most general representation of the matrix elements of equation (68) includes a many-body expansion with one-, two-, and three-body terms. However, only two conditions [(a) and (b) in equations (66), (67)] may be used in the determination of the one- and two-body energy terms. If more conditions were to exist, the dimension of the matrix necessary to represent the adiabatic potential would be larger.16 In what follows we shall argue that the definition of V12 must depend on the type of conical intersection, namely on whether its locus is finite or infinite in extent (Section II.C). For the cases of HzO and 03 [equations (66), (67)] the conical intersection occurs along the C projection line, but only for finite values of the molecular perimeter (for H20, there is also a simple intersection at the O + H2 asymptotic channel, which is avoided for finite values of the OH distances117). For example, one gets for the linear dissociation of 03... 

Dobbvn A.J. and Knowles P. (1997) A comparative study of methods for describing non-adiabatic coupling diabatic representation of the E+/ H HOH and HHO conical intersections. Mol. Phys. 91 1107-1 124 Dobbvn A.J. and Knowles P. (1998) General Discussion, Faraday Discuss. 110, 247. 

In this section, we describe an approach which, in addition to the implicit inclusion of the GP, takes into account all the non-adiabatic couplings between the two conically intersecting electronic surfaces. In this case, within the adiabatic representation, the nuclear Hamiltonian has the following form ... 

Fig. 11 Representation of lowest adiabatic potential of singlet (S = 0) and triplet (S = 1) Fe(CO)4 around T Jahn-Teller conical intersection at tetrahedral (7 ) geometry. There are three equivalent two-dimensional troughs in the space spanned by each pair-wise selection of equal L-M-L angles (boxed vs unboxed). The topological connectivity where the troughs intersect is indicated. There are two non-equivalent epikemel distortion directions E[ 2(Td,h) leading to 6 equivalent C2v minima ( ), and 12 equivalent Cs(x) saddle-points respectively. The non-Berry pseudo-rotation barrier is very small ( 5kcal mol ). CASSCF optimised geometrical parameters for singlet and triplet states are shown at the top left...

Under the conditions of validity of the two-electronically-adiabatic-state approximation it is possible to change from the i]/al,ad(r q) (n = i, j) electronically adiabatic representation to a diabatic one 1,ad(r q) (n = i, j) for which the VR Xn(R) terms in the corresponding diabatic nuclear motion equations are significantly smaller than in the adiabatic equation or, for favorable conditions, vanish [24-26]. Such an electronically diabatic representation is usually more convenient for scattering calculations involving two electronically adiabatic PESs, but not for those involving a single adiabatic PES. This matter will be further discussed in Sec. III.B.3 for the case in which a conical intersection between the E ad(q) and Ejad(q) PESs occurs. 

Let us now compare the characteristics of the electronically adiabatic and diabatic representations for systems displaying a conical intersection, in the one- and two-state approximations. 

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